Extending the Graph Formalism to Higher-Order Gates

2021/08/05 by Khesin, Andrey Boris, Ren, Kevin
#Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2108.02686

Abstract

We present an algorithm for efficiently simulating a quantum circuit in the graph formalism. In the graph formalism, we represent states as a linear combination of graphs with Clifford operations on their vertices. We show how a C₃ gate such as the Toffoli gate or \fracπ8 gate acting on a stabilizer state splits it into two stabilizer states. We also describe conditions for merging two stabilizer states into one. We discuss applications of our algorithm to circuit identities and finding low stabilizer rank representations of magic states.

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